Twisted Mass Research Articles

Insights on proton structure from lattice QCD: The twist-3 parton distribution function gT(x)

In this work, we present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution function $g_T(x)$ for the proton from lattice QCD. We use an ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3~fm, lattice spacing of 0.093~fm, and reproduces a pion mass of $260$ MeV. We use the quasi-distribution approach and employ three values of the proton momentum boost, 0.83 GeV, 1.25 GeV, and 1.67 GeV. We use a source-sink separation of 1.12~fm to suppress excited-states contamination. The lattice data are renormalized non-perturbatively. We calculate the matching equation within Large Momentum Effective Theory, which is applied to the lattice data in order to obtain $g_T$. The final distribution is presented in the $\overline{\rm MS}$ scheme at a scale of 2 GeV. We also calculate the helicity distribution $g_1$ to test the Wandzura-Wilczek approximation for $g_T$. We find that the approximation works well for a broad range of $x$. This work demonstrates the feasibility of accessing twist-3 parton distribution functions from novel methods within lattice QCD and can provide essential insights into the structure of hadrons.

Parton distribution functions from lattice QCD using Bayes-Gauss-Fourier transforms

We present a new method, based on Gaussian process regression, for reconstructing the continuous $x$-dependence of parton distribution functions (PDFs) from quasi-PDFs computed using lattice QCD. We examine the origin of the unphysical oscillations seen in current lattice calculations of quasi-PDFs and develop a nonparametric fitting approach to take the required Fourier transform. The method is tested on one ensemble of maximally twisted mass fermions with two light quarks. We find that with our approach oscillations of the quasi-PDF are drastically reduced. However, the final effect on the light-cone PDFs is small. This finding suggests that the deviation seen between current lattice QCD results and phenomenological determinations cannot be attributed solely on the Fourier transform.

Nucleon axial, tensor, and scalar charges and σ -terms in lattice QCD

We determine the nucleon axial, scalar and tensor charges within lattice Quantum Chromodynamics including all contributions from valence and sea quarks. We analyze three gauge ensembles simulated within the twisted mass formulation at approximately physical value of the pion mass. Two of these ensembles are simulated with two dynamical light quarks and lattice spacing $a=0.094$~fm and the third with $a=0.08$~fm includes in addition the strange and charm quarks in the sea. After comparing the results among these three ensembles, we quote as final values our most accurate analysis using the latter ensemble. For the nucleon isovector axial charge we find $1.286(23)$ in agreement with the experimental value. We provide the flavor decomposition of the intrinsic spin $\frac{1}{2}\Delta\Sigma^q$ carried by quarks in the nucleon obtaining for the up, down, strange and charm quarks $\frac{1}{2}\Delta\Sigma^{u}=0.431(8)$, $\frac{1}{2}\Delta\Sigma^{d}=-0.212(8)$, $\frac{1}{2}\Delta\Sigma^{s}=-0.023(4)$ and $\frac{1}{2}\Delta\Sigma^{c}=-0.005(2)$, respectively. The corresponding values of the tensor and scalar charges for each quark flavor are also evaluated providing valuable input for experimental searches for beyond the standard model physics. In addition, we extract the nucleon $\sigma$-terms and find for the light quark content $\sigma_{\pi N}=41.6(3.8)$~MeV and for the strange $\sigma_{s}=45.6(6.2)$~MeV. The y-parameter that is used in phenomenological studies we find $y=0.078(7)$.

Three photon decay of J/ψ from lattice QCD

Three photon decay rate of $J/\psi$ is studied using two $N_f=2$ twisted mass gauge ensembles with lattice spacings $a\simeq 0.085$ fm (I) and $0.067$ fm(II). Using a new method, only the correlation functions directly related to the physical decay width are computed with all polarizations of the initial and final states summed over. Our results for such rare decay on the two ensembles are: $\mathcal{B}_{I,II}(J/\psi\rightarrow 3\gamma)=(1.614 \pm 0.016 \pm 0.261)\times 10^{-5},(1.809 \pm 0.051 \pm 0.295)\times 10^{-5}$ where the first errors are statistical and the second are estimates from systematics. We also propose a method to analyze the Dalitz plot of the corresponding process based on the lattice data which can provide direct information for the experiments.

Ratios of the hadronic contributions to the lepton g−2 from lattice QCD+QED simulations

The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of an electron, muon, and $\ensuremath{\tau}$ lepton, ${a}_{\ensuremath{\ell}=e,\ensuremath{\mu},\ensuremath{\tau}}^{\mathrm{HVP},\mathrm{LO}}$, are computed using lattice $\mathrm{QCD}+\mathrm{QED}$ simulations. The results include the effects at order $\mathcal{O}({\ensuremath{\alpha}}_{em}^{2})$ as well as the electromagnetic and strong isospin-breaking corrections at orders $\mathcal{O}({\ensuremath{\alpha}}_{em}^{3})$ and $\mathcal{O}({\ensuremath{\alpha}}_{em}^{2}({m}_{u}\ensuremath{-}{m}_{d}))$, respectively, where $({m}_{u}\ensuremath{-}{m}_{d})$ is the $u$- and $d$-quark mass difference. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration with ${N}_{f}=2+1+1$ dynamical quarks at three values of the lattice spacing ($a\ensuremath{\simeq}0.062$, 0.082, 0.089 fm) with pion masses in the range $\ensuremath{\simeq}210--450\text{ }\text{ }\mathrm{MeV}$. The calculations are based on the quark-connected contributions to the HVP in the quenched-QED approximation, which neglects the charges of the sea quarks. The quark-disconnected terms are estimated from results available in the literature. We show that in the case of the electron-muon ratio the hadronic uncertainties in the numerator and in the denominator largely cancel out, while in the cases of the electron-$\ensuremath{\tau}$ and muon-$\ensuremath{\tau}$ ratios such a cancellation does not occur. For the electron-muon ratio we get ${R}_{e/\ensuremath{\mu}}\ensuremath{\equiv}({m}_{\ensuremath{\mu}}/{m}_{e}{)}^{2}({a}_{e}^{\mathrm{HVP},\mathrm{LO}}/{a}_{\ensuremath{\mu}}^{\mathrm{HVP},\mathrm{LO}})=1.1456(83)$ with an uncertainty of $\ensuremath{\simeq}0.7%$. Our result, which represents an accurate Standard Model (SM) prediction, agrees very well with the estimate obtained using the results of dispersive analyses of the experimental ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}$ hadrons data. Instead, it differs by $\ensuremath{\simeq}2.7$ standard deviations from the value expected from present electron and muon ($g\ensuremath{-}2$) experiments after subtraction of the current estimates of the QED, electroweak, hadronic light-by-light and higher-order HVP contributions, namely ${R}_{e/\ensuremath{\mu}}=0.575(213)$. An improvement of the precision of both the experiment and the QED contribution to the electron ($g\ensuremath{-}2$) by a factor of $\ensuremath{\simeq}2$ could be sufficient to reach a tension with our SM value of the ratio ${R}_{e/\ensuremath{\mu}}$ at a significance level of $\ensuremath{\simeq}5$ standard deviations.

Lattice study of form factors for charmonium

Form factors for $$\eta _c$$ and $$\chi _{c0}$$ have been simulated based on $$N_f=2$$ Twisted Mass Lattice Quantum Chromodynamics (Lattice QCD) gauge configurations. We construct particle interpolation operators by variational method that can significantly improve signal-to-noise ratio of correlation functions. We apply twisted boundary conditions to compute corresponding correlation functions which make us obtain form factors with more small four-momentum transfer. Furthermore, we fit charge radius for $$\eta _c$$ and $$\chi _{c0}$$ , respectively. The results obtained in this simulation could be considered as a ground test to calculate branch ratio decay width of $$\chi _{c0,1,2}\rightarrow {\gamma {J/\psi }}$$ on lattice in future.

Ward identity of the vector current and the decay rate of ηc→γγ in lattice QCD

Using a recently proposed method arXiv:1910.11597 (Yu Meng et al.), we study the two-photon decay rate of $\eta_c$ using two $N_f=2$ twisted mass gauge ensembles with lattice spacings $0.067$fm and $0.085$fm. The results obtained from these two ensembles can be extrapolated in a naive fashion to the continuum limit, yielding a result that is consistent with the experimental one within two standard deviations. To be specific, we obtain the results for two-photon decay of $\eta_c$ as $\mathcal{B}(\eta_c\rightarrow 2\gamma)= 1.29(3)(18)\times 10^{-4}$ where the first error is statistical and the second is our estimate for the systematic error caused by the finite lattice spacing. It turns out that Ward identity for the vector current is of vital importance within this new method. We find that the Ward identity is violated for local current with a finite lattice spacing, however it will be restored after the continuum limit is taken.

Parton distribution functions of Δ+ on the lattice

We perform a first calculation for the unpolarized parton distribution function of the $\Delta^+$ baryon using lattice QCD simulations within the framework of Large Momentum Effective Theory. Two ensembles of $N_f=2+1+1$ twisted mass fermions are utilized with a pion mass of 270 MeV and 360 MeV, respectively. The baryon, which is treated as a stable single-particle state, is boosted with momentum $P_3$ with values $\{0.42,0.83,1.25\}$ GeV, and we utilize momentum smearing to improve the signal. The unpolarized parton distribution function of $\Delta^+$ is obtained using a non-perturbative renormalization and a one-loop formula for the matching, with encouraging precision. In particular, we compute the $\overline{d}(x)-\overline{u}(x)$ asymmetry and compare it with the same quantity in the nucleon, in a first attempt towards resolving the physical mechanism responsible for generating such asymmetry.

Lattice study of two-photon decay widths for scalar and pseudo-scalar charmonium * * This work is supported in part by the National Science Foundation of China (NSFC) (11335001, 11275169, 11405178, 11935017, 11575196, 11875169, 11775229). It is also supported in part by the DFG and the NSFC (11261130311) through funds provided to the Sino-Germen CRC 110 symmetries and the Emergence of

This exploratory study computes two-photon decay widths of pseudo-scalar ( ) and scalar ( ) charmonium using two ensembles of twisted mass lattice QCD gauge configurations. The simulation is performed using two lattice ensembles with lattice spacings fm with size and fm with size . The decay widths for the two charmonia are obtained within the expected ballpark, but are however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.

Model-independent determination of the nucleon charge radius from lattice QCD

Lattice QCD calculations of nucleon form factors are restricted to discrete values of the Euclidean four-momentum transfer. Therefore, the extraction of radii typically relies on parametrizing and fitting the lattice QCD data to obtain its slope close to zero momentum transfer. We investigate a new method, which allows to compute the nucleon radius directly from existing lattice QCD data, without assuming a functional form for the momentum dependence of the underlying form factor. The method is illustrated for the case of the isovector mean-square charge radius of the nucleon $⟨{r}_{\mathrm{isov}}^{2}⟩$ and the quark-connected contributions to $⟨{r}_{p}^{2}⟩$ and $⟨{r}_{n}^{2}⟩$ for the proton and neutron, respectively. Computations are performed using a single gauge ensemble with ${N}_{f}=2+1+1$ maximally twisted mass clover-improved fermions at physical quark mass and a lattice spacing of $a=0.08\text{ }\text{ }\mathrm{fm}$.

Comparison of topological charge definitions in Lattice QCD

In this paper, we show a comparison of different definitions of the topological charge on the lattice. We concentrate on one small-volume ensemble with 2 flavours of dynamical, maximally twisted mass fermions and use three more ensembles to analyze the approach to the continuum limit. We investigate several fermionic and gluonic definitions. The former include the index of the overlap Dirac operator, the spectral flow of the Wilson–Dirac operator and the spectral projectors. For the latter, we take into account different discretizations of the topological charge operator and various smoothing schemes to filter out ultraviolet fluctuations: the gradient flow, stout smearing, APE smearing, HYP smearing and cooling. We show that it is possible to perturbatively match different smoothing schemes and provide a well-defined smoothing scale. We relate the smoothing parameters for cooling, stout and APE smearing to the gradient flow time tau . In the case of hypercubic smearing the matching is performed numerically. We investigate which conditions have to be met to obtain a valid definition of the topological charge and susceptibility and we argue that all valid definitions are highly correlated and allow good control over topology on the lattice.

Twisted mass transport enabled by the angular momentum of light

Light may carry both orbital angular momentum (AM) and spin AM. The former is a consequence of its helical wavefront, and the latter is a result of its rotating transverse electric field. Intriguingly, the light–matter interaction with such fields shows that the orbital AM of light causes a physical “twist” in a range of materials, including metal, silicon, azopolymer, and even liquid-phase resin. This process may be aided by the light’s spin AM, resulting in the formation of various helical structures. The exchange between the AM of light and matter offers not only unique helical structures at the nanoscale but also entirely novel fundamental phenomena with regard to the light–matter interaction. This will lead to the future development of advanced photonics devices, including metamaterials for highly sensitive detectors as well as reactions for chiral chemical composites. Here, we focus on interactions between the AM of light and azopolymers, which exhibit some of the most diverse structures and phenomena observed. These studies result in helical surface relief structures in azopolymers and will leverage next-generation applications with light fields carrying optical AM.

Moments of nucleon generalized parton distributions from lattice QCD simulations at physical pion mass

We present results for the moments of nucleon isovector vector and axial generalised parton distribution functions computed within lattice QCD. Three ensembles of maximally twisted mass clover-improved fermions simulated with a physical value of the pion mass are analyzed. Two of these ensembles are generated using two degenerate light quarks. A third ensemble is used having, in addition to the light quarks, strange and charm quarks in the sea. A careful analysis of the convergence to the ground state is carried out that is shown to be essential for extracting the correct nucleon matrix elements. This allows a controlled determination of the unpolarised, helicity and tensor second Mellin moments. The vector and axial-vector generalised form factors are also computed as a function of the momentum transfer square up to about 1 GeV$^2$. The three ensembles allow us to check for unquenching effects and to assess lattice finite volume effects.

Electromagnetic form factor of Ds∗ meson from Nf = 2 twisted mass lattice QCD

We investigate the electromagnetic form factor of [Formula: see text] meson using [Formula: see text] twisted mass lattice quantum chromodynamics gauge configurations. The numerical simulations are carried out under twisted boundary conditions which are helpful to increase the resolution in momentum space. We determine electromagnetic form factors with more small four-momentum transfer, and further fit the charge radius for [Formula: see text] meson.

Erratum: Scalar and vector form factors of D→π(K)ℓν decays with Nf=2+1+1 twisted fermions [Phys. Rev. D 96 , 054514 (2017)

We present a lattice determination of the vector and scalar form factors of the $D \to \pi(K) \ell \nu$ semileptonic decays, which are relevant for the extraction of the CKM matrix elements $|V_{cd}|$ and $|V_{cs}|$ from experimental data. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with $N_f = 2+1+1$ flavors of dynamical quarks, at three different values of the lattice spacing and with pion masses as small as 210 MeV. The matrix elements of both vector and scalar currents are determined for a plenty of kinematical conditions in which parent and child mesons are either moving or at rest. Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum limit we determine the vector and scalar form factors in the whole kinematical region from $q^2 = 0$ up to $q^2_{max} = (M_D - M_{\pi(K)})^2$ accessible in the experiments, obtaining a good overall agreement with experiments, except in the region at high values of $q^2$ where some deviations are visible. A set of synthetic data points, representing our results for $f_+^{D \pi(K)}(q^2)$ and $f_0^{D \pi(K)}(q^2)$ for several selected values of $q^2$, is provided and also the corresponding covariance matrix is available. At zero 4-momentum transfer we get: $f_+^{D \to \pi}(0) = 0.612 ~ (35)$ and $f_+^{D \to K}(0) = 0.765 ~ (31)$. Using the experimental averages for $|V_{cd}| f_+^{D \to \pi}(0)$ and $|V_{cs}| f_+^{D \to K}(0)$, we extract $|V_{cd}| = 0.2330 ~ (137)$ and $|V_{cs}| = 0.945 ~ (38)$, respectively. The second-row of the CKM matrix is found to be in agreement with unitarity within the current uncertainties: $|V_{cd}|^2 + |V_{cs}|^2 + |V_{cb}|^2 = 0.949 ~ (78)$.

Exact WKB analysis of \u2102\u21191 holomorphic blocks

We study holomorphic blocks in the three dimensional mathcal{N} = 2 gauge theory that describes the ℂℙ1 model. We apply exact WKB methods to analyze the line operator identities associated to the holomorphic blocks and derive the analytic continuation formulae of the blocks as the twisted mass and FI parameter are varied. The main technical result we utilize is the connection formula for the 1\U0001d7191q-hypergeometric function. We show in detail how the q-Borel resummation methods reproduce the results obtained previously by using block-integral methods.

A coupled-channel lattice study of the resonance-like structure Zc(3900) * * Supported in part by the Ministry of Science and Technology of China (MSTC) under 973 project "Systematic studies on light hadron spectroscopy" (2015CB856702). It is also supported in part by the DFG and the NSFC through funds provided to the Sino-Germen CRC 110 "Symmetries and the Emergence of Structure

In this exploratory study, near-threshold scattering of D and meson is investigated using lattice QCD with twisted mass fermion configurations. The calculation is performed in the coupled-channel Lüscher finite-size formalism. The study focuses on the channel with where the resonance-like structure was discovered. We first identify the two most relevant channels and the lattice study is performed in the two-channel scattering model. Combined with the two-channel Ross-Shaw theory, scattering parameters are extracted from the energy levels by solving the generalized eigenvalue problem. Our results for the scattering length parameters suggest that for the particular lattice parameters that we studied, the best fit parameters do not correspond to the peak in the elastic scattering cross-section near the threshold. Furthermore, in the zero-range Ross-Shaw theory, the scenario of a narrow resonance close to the threshold is disfavored beyond the 3 level.

Light-meson leptonic decay rates in lattice QCD+QED

The leading electromagnetic (e.m.) and strong isospin-breaking corrections to the $\pi^+ \to \mu^+ \nu[\gamma]$ and $K^+ \to \mu^+ \nu[\gamma]$ leptonic decay rates are evaluated for the first time on the lattice. The results are obtained using gauge ensembles produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks. The relative leading-order e.m.~and strong isospin-breaking corrections to the decay rates are 1.53(19)\% for $\pi_{\mu 2}$ decays and 0.24(10)\% for $K_{\mu 2}$ decays. Using the experimental values of the $\pi_{\mu 2}$ and $K_{\mu 2}$ decay rates and updated lattice QCD results for the pion and kaon decay constants in isosymmetric QCD, we find that the Cabibbo-Kobayashi-Maskawa matrix element $ | V_{us}| = 0.22538(46)$, reducing by a factor of about $1.8$ the corresponding uncertainty in the Particle Data Group review. Our calculation of $|V_{us}|$ allows also an accurate determination of the first-row CKM unitarity relation $| V_{ud}|^2 + | V_{us}|^2 + | V_{ub}|^2 = 0.99988(46)$. Theoretical developments in this paper include a detailed discussion of how QCD can be defined in the full QCD+QED theory and an improved renormalisation procedure in which the bare lattice operators are renormalised non-perturbatively into the (modified) Regularization Independent Momentum subtraction scheme and subsequently matched perturbatively at $O(\alpha_{em}\alpha_s(M_W))$ into the W-regularisation scheme appropriate for these calculations.

Proton and neutron electromagnetic form factors from lattice QCD

The electromagnetic form factors of the proton and the neutron are computed within lattice QCD using simulations with quarks masses fixed to their physical values. Both connected and disconnected contributions are computed. We analyze two new ensembles of $N_f = 2$ and $N_f = 2 + 1 + 1$ twisted mass clover-improved fermions and determine the proton and neutron form factors, the electric and magnetic radii, and the magnetic moments. We use several values of the sink-source time separation in the range of 1.0 fm to 1.6 fm to ensure ground state identification. Disconnected contributions are calculated to an unprecedented accuracy at the physical point. Although they constitute a small correction, they are non-negligible and contribute up to 15% for the case of the neutron electric charge radius.

How much do charm sea quarks affect the charmonium spectrum?

The properties of charmonium states are or will be intensively studied by the B-factories Belle II and BESIII, the LHCb and PANDA experiments and at a future Super-c-tau Factory. Precise lattice calculations provide valuable input and several results have been obtained by simulating up, down and strange quarks in the sea. We investigate the impact of a charm quark in the sea on the charmonium spectrum, the renormalization group invariant charm–quark mass M_{mathrm{c}} and the scalar charm–quark content of charmonium. The latter is obtained by the direct computation of the mass-derivatives of the charmonium masses. We do this investigation in a model, QCD with two degenerate charm quarks. The absence of light quarks allows us to reach very small lattice spacings down to 0.023~hbox {fm}. By comparing to pure gauge theory we find that charm quarks in the sea affect the hyperfine splitting at a level around 2%. The most significant effects are 5% in M_c and 3% in the value of the charm quark content of the eta _c meson. Given that we simulate two charm quarks these estimates are upper bounds for the contribution of a single charm quark. We show that lattice spacings <0.06~hbox {fm} are needed for safe continuum extrapolations of the charmonium spectrum with O(a) improved Wilson quarks. A useful relation for the projection to the desired parity of operators in two-point functions computed with twisted mass fermions is proven.